2824 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 12, DECEMBER 2014 Enhanced Interpolated-DFT for Synchrophasor Estimation in FPGAs: Theory, Implementation, and Validation of a PMU Prototype Paolo Romano, Student Member, IEEE, and Mario Paolone, Senior Member, IEEE Abstract— The literature on the subject of synchrophasor estimation (SE) algorithms has discussed the use of interpolated discrete Fourier transform (IpDFT) as an approach capable to find an optimal tradeoff between SE accuracy, response time, and computational complexity. Within this category of algorithms, this paper proposes three contributions: 1) the formulation of an enhanced-IpDFT (e-IpDFT) algorithm that iteratively compensates the effects of the spectral interference produced by the negative image of the main spectrum tone; 2) the assessment of the influence of the e-IpDFT parameters on the SE accuracy; and 3) the discussion of the deployment of IpDFT- based SE algorithms into field programmable gate arrays, with particular reference to the compensation of the error introduced by the free-running clock of A/D converters with respect to the global positioning system (GPS) time reference. The paper finally presents the experimental validation of the proposed approach where the e-IpDFT performances are compared with those of a classical IpDFT approach and to the accuracy requirements of both P and M-class phasor measurement units defined in the IEEE Std. C37.118-2011. Index Terms— Discrete Fourier transform (DFT), field programmable gate array (FPGA), IEEE Std. C37.118, interpolated discrete Fourier transform (IpDFT), phasor measurement unit (PMU), synchrophasor. I. I NTRODUCTION T HE core component of a phasor measurement unit (PMU) is represented by the synchrophasor estimation (SE) algorithm, whose choice is driven by three main factors: 1) its accuracy; 2) its response times; and 3) its computational complexity [1]. Concerning points 1) and 2) PMUs need to be com- pliant with the requirements imposed by the IEEE Std. C37.118.1-2011 [2]. This standard defines synchrophasor, fre- quency, and rate of change of frequency (ROCOF) measure- ments as well as accuracy limits for the majority of operating conditions under both steady-state and dynamic conditions. In this respect, the above mentioned IEEE Std. has also intro- duced the well-known PMU performance classes P and M. Manuscript received December 17, 2013; revised April 11, 2014; accepted April 12, 2014. Date of publication April 30, 2014; date of current version November 6, 2014. This work was supported by the European Commu- nity’s Seventh Framework Programme FP7-ICT-2011-8 under Grant 318708 through C-DAX. The Associate Editor coordinating the review process was Dr. Dario Petri. The authors are with the Distributed Electrical System Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland (e-mail: paolo.romano@epfl.ch; mario.paolone@epfl.ch). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIM.2014.2321463 In particular, class-P PMUs are devices whose applications require fast response and no explicit filtering (i.e., power systems protections), whereas class-M PMUs are devices intended for applications that could be undesirably effected by aliased signals and do not require a fast response time. As known, the main task of a SE algorithm is to assess the parameters of the fundamental tone of a signal using a previously acquired set of samples representing a portion of an acquired waveform (i.e., node voltage and/or branch/nodal current). For this reason, points 1) and 2) are inherently cou- pled and, usually, better accuracies imply larger response times and vice versa. In addition, as the phasor is, by definition, a static representation of a sinusoidal waveform, the SE might be largely biased when the grid frequency drifts from the nominal one and, more generally, during network dynamic conditions. To cope with 1) and 2), different techniques have been proposed as summarized below. Typically, most of the SE algorithms are based on the direct implementation of the discrete Fourier transform (DFT), or its algorithmic version—fast Fourier transform (FFT)—applied to quasi-steady state signals. Based on the window length, DFT-based algorithms can be grouped into multicycle, one-cycle, or fractional-cycle DFT estimators performing recursive and nonrecursive updates [3]–[5]. To improve their accuracy, DFT-based algorithms can be used in combina- tion with weighted least-squares [6] or Kalman filter-based methods [7]. Non-DFT-based SE methods have also been proposed. These include wavelet-based algorithms [8] and those based on the more recent dynamic phasor concept. The latter have been proposed stand-alone [9] or in combi- nation with other techniques like, for instance, signal sub- space [10], weighted least-squares [11], [12] or adaptive filters methods [13]. Within the category of DFT-based SE algorithms, to achieve an optimal tradeoff between the estimation accu- racy and response time, the use of time-windows in com- bination with the well-known interpolated-discrete Fourier transform (IpDFT) technique has been first proposed in [14] and [15] and further developed in [16]–[19]. More in par- ticular, contributions [18] and [19] have proven that the effects of long and short-range leakage can be considerably minimized by adopting suitable windows functions and IpDFT schemes, respectively, [20], [21]. The advantages of this kind of approaches refer to the relatively simple implementation and low-computational complexity capable of achieving reasonable 0018-9456 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.